Discussions

Use a proper battery pack or a suitable LED.What you want is not really feasable and will not really be good for the lifespan of your battery.If you need 5V you also need a converter that reduces the max power a little bit.Makes me wonder why people always want to go overboard with LED's these days...

LEDs have drop voltages around 3.2V or so, which is about how low you can safely discharge a lithium ion battery to! battery capacity is really a difficult thing to calculate accurately. The easiest way is to simply assume that you can derive the WH rating of the battery from the mAH or AH rating you see. Problem is though is that the voltage of the battery will change as it is discharged, and the discharge curve will depend on many, MANY factors, like the rate of discharge, the type of discharge (constant resistance, constant current, or constant power, or something more complicated?), the temperature, etc etc etc.

To calculate roughly how long your LED will be powered, you will need to first look into the LED driver you plan to use, if any. You will need to consider how much current the LED draws as a function of the voltage applied to it. Most good drivers will be roughly constant power, meaning that as the voltage applied to the driver sags, the current that it pulls will increase, such that the product of the voltage and current is constant. (hence the term, constant power load.) Once you know that, you need to find a discharge curve of the battery as close as possible to that 5W load, and then take the definite integral of that curve (figure out the area under the curve) to figure out the WH capacity. That can be done by drawing lots of thin tall rectangles inside the curve and adding up all the rectangle area's. Alternatively, you can import the data into a spreadsheet and calculate the WH that way. Then just extrapulate that WH figure to the load to see how long it will be powered. WH / W = H.

Even my phone cannot accurately judge how much charge is in the battery, when the percentage falls below 10%, the percentage starts dropping like a brick wall as I use my phone, it will within a minute or so get down to 1%, but if I stop using my phone, warm it up in a hot car, and/or just leave it alone, the apparent charge will climb back up to 15% or so! Similarly in cold weather the battery percentage is lower than it should be. That is because the voltage of the battery will recover slightly when not under load, (basicly it is like if you are working hard, outputting lots of work, and you get really tired and lose strength, until you are allowed to catch your breath. Same with batteries.)